1. Field of the Invention
The present invention relates to a method of machining a workpiece three-dimensionally with a machine tool such as a milling cutter, and more particularly to a calculation control for generating a path of the machine tool.
2. Description of Related Art
Recently, computerized three-dimensional machining has been developed for practical use.
In the machining, a computer calculates a path of the center of a machine tool, and the tool moves in accordance with the calculated path to machine a surface.
A surface to be machined is defined by control factors, and a path of the tool center is calculated from the control factors. Then, the tool follows the calculated path. In a conventional method, three-dimensional data are used for accurate machining. More specifically, every cheek point on the surface to be machined is defined by x, y and z coordinates, and the three-dimensional data on all the points are stored in the computer. Then, a path of the tool center is calculated from the data, and the tool or a workpiece is moved to follow the path.
The tool center path calculation is based on intersection calculation. Calculation of the intersection of a line and a curved surface is herewith described. Generally, a curved surface cannot be entirely expressed by a single equation. FIG. 30 shows a conventional method of intersection calculation. A curved surface #s is divided into small planes (polygons) 1, 2, 3 - - - n, and every polygon is checked whether to intersect a line 1. In the example of FIG. 30, the intersection of the line 1 and the surface #s is located in polygon 21. In this way, where a curved surface intersects a line is figured out. In order to improve the accuracy of machining which uses the intersection calculation, a curved surface must be divided into as small polygons as possible. However, this results in charging the computer with such an enormous volume of processing that a 16-bit computer cannot handle or that even a large computer takes a long time to complete.
The volume of processing handled by the computer must be in accordance with the accuracy of the machine tool. If the machine tool has a low accuracy, minute calculation through an enormous volume of processing will be in vain. On the other hand, if the machine tool has a high accuracy, the computer must be large enough to make minute calculation, though the large computer cannot increase the machining speed.
Another issue in the machining is transference of machining from a surface to another. Referring to FIG. 31, it is a big issue at what timing the machine tool transfers from a path along a surface #i (indicated with arrow a) to a path along a surface #j. Conventionally, the z values of the surface #i and the surface #j are compared at every check point, and the machining is progressed along the surface which has a larger or a smaller z value. Whether selecting a larger z value or a smaller z value depends on the program preset by the operator. Additionally, tool interference must be checked at every check point. Thus, since the processing must be performed at every check point, the calculation speed is low. Moreover, the transference of machining cannot be performed at the accurate timing. Referring to FIG. 31, when the center of the machine tool comes to a cheek point: P.sub.1, the machine tool will interfere with the surface #j, that is, the machine tool will make a recession on the surface #j. When the center of the machine tool comes to a check point P.sub.2, the machine tool will interfere with the surface #1. Therefore the transference of machining from the surface #i to the surface #j starts at a cheek point Pa immediately before the point P.sub.2 and finishes at a point P.sub.4 where the interference of the machine tool with the surface #i will not occur. In this way, however, the shadowed area in FIG. 31 is left unmachined.